PrimeOmega

PrimeOmega[n]

gives the number of prime factors counting multiplicities in n.

Details and Options

  • Integer mathematical function, suitable for both symbolic and numerical manipulation.
  • For a number with a unit and primes, PrimeOmega[n] returns k1+⋯+km.
  • PrimeOmega[n,GaussianIntegers->True] gives the number of Gaussian prime factors in n.
  • PrimeOmega is a completely additive number theoretic function.

Examples

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Basic Examples  (2)

gives the number of prime factors counting multiplicities:

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Plot the sequence:

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Scope  (4)

Options  (1)

Properties & Relations  (3)

Introduced in 2008
(7.0)